1. A levitated nanocryostat: Laser refrigeration, alignment and rotation of Yb3+ : YLF nanoparticles
A. T. M. Anishur Rahman & Peter F. Barker
Department of Physics & Astronomy
University College London
London, UK

2. Outline UCL optomechanics – an overview Introduction to laser cooling
Motivation behind laser refrigeration
Cooling the internal temp. of levitated Yb3+:YLF nanocrystals
Birefringence of Yb3+:YLF -
Rotation in CP light and alignment in LP light
Parametric feedback cooling
Conclusions

3. Main objective of our experiments
Creating/Generating different non- classical states such as –
the motional ground states
Schrodinger cat states

4. Main challenge - decoherence1
High CM temperature
<𝑛> = 𝑇 𝐶𝑀 ℎ𝜔
Quantum system
Collision with background gas
𝜏𝑔=ℎ𝜔/𝛾𝑔𝑘𝐵𝑇𝑐𝑚
Recoil heating
𝜏𝑟∝1/𝐼
Blackbody emission
∝𝑇5
1. Chang et al. PNAS 2010.

5. UCL Optomechanics Experiments Dipole trap Hybrid trap Paul trap
Creating non-classical states i.e. motional ground state
Dipole trap
Laser refrigeration, parametric feedback cooling
Hybrid trap
Cavity + Paul trap
Cavity cooling
Paul trap
Nanodiamond with NV centres

6. Laser refrigeration Controlling the internal temperature
of a material using laser only
Similar to laser cooling of atoms
but it uses anti-Stokes fluorescence
for controlling the internal temp

7. Laser refrigeration -motivations
Enabling fundamental physics experiments i.e.
by increasing the spin coherence time of NV centres
in appropriately engineered levitated nanodiamond
Solving existing problems of burning/melting
of nanoparticles in dipole trap1,2,3
Rahman et al. Sci. Rep. (2016).
Millen et al. Nat. Nano. (2014).
Hoang et al, Nat. Comm. (2016)

8. Conditions for optical refrigeration
Anti-Stokes fluorescence (λf< λ)
Energy gap between levels ∆𝐸<𝑘𝐵𝑇
High quantum efficiency
Phonon energy of host materials
must be low < kBT
Rapid thermalization of population
in excited state (normally in ps)
Excited state lifetime should be
longer than thermalization time λ λf

9. Anti-Stokes fluorescence from levitated Yb3+: YLF nanocrystals

10. Internal temp. of levitated Yb3+:YLF naonocrystals
Temp. from Boltzmann distr 𝑇 = 1 𝑇0 + 𝑘𝐵 ∆𝐸65 ln 𝑅 𝑅0 , where
𝑅= 𝐼(𝐸6 →𝐸1) 𝐼(𝐸5 →𝐸2) @ T and 𝑅0= 𝐼(𝐸6 →𝐸1) 𝐼(𝐸5 →𝐸2) @ T0
A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

11. A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).
Temperature from PSD
Power spectral density – 𝑆 𝑥 (𝜔)= 2𝑘𝐵𝑇 𝑀 𝛾 𝜔2−𝜔02 2+𝛾2𝜔2
Temperature and damping
are related as - 𝑇∝ 𝛾2
Assuming T1064 nm= 255 K,
𝑇 𝑛𝑚 = 𝑇 1064 𝑛𝑚 𝛾 1031 𝑛𝑚 2 𝛾 1064 𝑛𝑚 2
=171±21 K
A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

12. Blackbody emission and it’s consequence
Plank’s law of blackbody emission
𝐼 𝜔 = ℎ𝜔3 𝜋2𝑐2( 𝑒 ℎ𝜔 𝑘𝐵𝑇 −1)
Damping rate due to blackbody emission -
𝛾𝐵𝐵 ∝(𝑅BB/𝜔𝑚 )
where 𝑅𝐵𝐵= 𝐼 𝜔 𝑑𝜔 .
Number of oscillations before the oscillator excites by one quanta –
1/𝛾𝐵𝐵 ∝(𝜔𝑚/𝑅BB )

13. Given right laser and proper nanoparticles
We can reach 50 K
which is about 4 orders magnitude blackbody suppression

14. Thermodynamic simulation
Heating rate due to collisions with gas molecules – 𝑞 ℎ = 8𝜋 𝑎 2 𝑘 𝑔 2𝑎+Λ𝐺 ∆𝑇, where a is the radius, Λ is the mean free path of air molecules, kg is thermal conductivity of air, G=(18γ-10)/A(γ+1) , A is the accommodation coefficient of air and ∆𝑇 is the difference in temperature between the air molecules and levitated particles.
Cooling rate due to anti-Stokes fluorescence - 𝑞 𝑐 =𝑉𝛼𝐼(1−η𝑞 λ λ𝑓 ), where V is the volume of the nanoparticle, 𝛼 is the absorption coefficient, I is the laser intensity, η𝑞 quantum efficiency, λ𝑓 is the average fluorescence wavelength and λ is the excitation wavelength.
Setting qh=qc at equilibrium, we get T≈200 K
A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

15. Birefringence of Yb3+:YLF : self orientation
Two orientations a // E & c // E
Fluorescence and temp.
depends on crystal orientation
Trapping power > 50 mW : c // E
Trapping power < 50 mW : a // E
A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

16. Birefringence of Yb3+:YLF - rotation & pendular motion3
Pendular motion in linearly polarized light (Fig. a & d)
Rotation in circularly polarized light (Fig. b & c)
ATM A. Rahman and P. F. Barker, Nat. Photon. (2017).

17. Parametric feedback cooling
It controls the CM motion of a levitated nanoparticle
Has been successfully used to reach sub-millikelvin CM temperature1
Ground state how far or is it needed???

18. Joint CM & internal temperatures control
Work in progress

19. Conclusions
Internal temperature can be controlled using anti- Stokes fluorescence
Internal temperature as low as 130 K has been achieved.
Blackbody emission has been suppress by approx. four orders of magnitude
Birefringent Yb3+:YLF particles rotate in CP & LP light